I don't think fitting in platforms is a big problem because they would only needed in one direction. I think if 501 and 510 were converted to modern LRT like this a lot of stops would be removed anyways. As for left turns, they are already banned along parts of Queen and King anyways, and some interesections have space for left turn lanes.
I assume you mean 501 and 504?
The additional width for platforms and left turn lanes would be one lane's worth. It would be left turn lane on nearside, platform on far side. True, it's not that much (3.2m), but there isn't that much width to begin with.
For the most part, the King and Queen have a 20m right of way, from building front to building front.
Fitting a 5 lane, 16m roadway into a 20m ROW only leaves 2m on each side. That space must be used for a large number of functions, such as sidewalks, benches, transit shelters, utility poles... That might be OK in a suburban environment, but is completely unacceptable on major shopping streets.
As you say, there are a few places where the ROW widens (such as Queen at Spadina), but these are not common enough to account for the required turn lanes and platforms.
So, it would have to be at most 1 through car lane on each street.
I'm convinced that trying to compromise between transit and car space will end up just causing delays for both, and end up screwing over cyclists in the process. Cycling on your redesigned streets would be even less pleasant than it currently is to cycle on King or Queen.